2. Jack’s parents were planning a big birthday party for him. Answer the questions below. Show your work for all parts.
a. His parents spent $4.49 on each of 6 goodie bags. How much did they spend on goodie bags?

b. They spent $150 to rent a bounce house for 8 hours. How much is the hourly rate for the rental?


c. If the parents spent a total of $400 on everything for the party, how much more did they spend in addition to what was spent in parts (a) and (b)?

The area of the shaded region is equal to 45 square units.

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LW

Where:

By substituting the given side lengths into the formula for the area of a rectangle, we have the following;

Area of rectangle = 8 × 6

Area of rectangle = 48 square units.

Since the opposite sides of any rectangle are congruent (equal), the legs of the right triangle can be calculated as follows;

L₁ = 8 - 5 = 3 units.

L₂ = 6 - 4 = 2 units.

Area of right triangle = 1/2 × 3 × 2

Area of right triangle = 3 square units.

For the area of the shaded region, we have:

Area of the shaded region = 48 square units - 3 square units.

Area of the shaded region = 45 square units.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The arrow is at a height of 48 ft after approx. 3 - √6 s and after 3 + √6 s.

To find the time it takes for the arrow to reach a height of 48 ft, we can use the formula for the height of the arrow:

s = v0t - 16t^2

Here, s represents the height of the arrow, v0 is the initial velocity, and t is the time.

Given that the initial velocity, v0, is 96 ft/s and the height, s, is 48 ft, we can set up the equation:

48 = 96t - 16t^2

Now, let's solve this equation to find the time it takes for the arrow to reach a height of 48 ft.

Rearranging the equation:

16t^2 - 96t + 48 = 0

Dividing the equation by 16 to simplify:

t^2 - 6*t + 3 = 0

We now have a quadratic equation in the form of at^2 + bt + c = 0, where a = 1, b = -6, and c = 3.

Using the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values:

t = (6 ± √((-6)^2 - 413)) / (2*1)

t = (6 ± √(36 - 12)) / 2

t = (6 ± √24) / 2

Simplifying the square root:

t = (6 ± 2√6) / 2

t = 3 ± √6

Therefore, the arrow reaches a height of 48 ft after approximately 3 + √6 seconds and 3 - √6 seconds.

In summary, the arrow takes approximately 3 + √6 seconds and 3 - √6 seconds to reach a height of 48 ft, assuming an initial velocity of 96 ft/s.

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Note the complete question is

The height of an arrow shot upward can be given by the formula s = v0*t - 16*t², where v0 is the initial velocity and t is time.How long does it take for the arrow to reach a height of 48 ft if it has an initial velocity of 96 ft/s?  

Solve (t-3)^2=6

The arrow is at a height of 48 ft after approx. ___ s and after ___ s.

Answer: I want to say 3/4

Step-by-step explanation:

The amount that can be withdrawn immediately after the last deposit is approximately $8,876.80.

We can use the formula for the future value of an ordinary annuity. The formula is given by:

\(FV = P * [(1 + r/n)^(^n^t^) - 1] / (r/n)\)

Where

Given:

Plugging in the values, we have:

\(FV = 480 * [(1 + 0.045/2)^(^2*^8^) - 1] / (0.045/2)\)

Calculating the expression inside the brackets

\((1 + 0.045/2)^(^2^*^8^) = 1.0225^1^6\)≈ 1.4197

Substituting this value back into the formula:

FV = 480 * (1.4197 - 1) / (0.045/2)

FV = 480 * 0.4197 / 0.0225

FV ≈ $8,876.80

So, the amount that can be withdrawn immediately after the last deposit is approximately $8,876.80.

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Answer: 1/15 of his money

Step-by-step explanation:

give them a common denominator (15) and then subtract then number from 15/15

Step-by-step explanation:

please mark me as brainlest

Answer:

x=5 and y=2

Step-by-step explanation:

I hope this helps

The measure of the angle A is 70 degrees if the DR is the tangent to the circle option (A) 70 degrees is correct.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

It is given that:

Join the points B and O and then join points D and O

Angle A = (1/2)Angle BOD

Angle B = 140 degrees

Angle A = (1/2)140 degrees

Angle A = 70 degrees

Thus, the measure of the angle A is 70 degrees if the DR is the tangent to the circle option (A) 70 degrees is correct.

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let's take a peek at the picture above, hmmm let's notice the vertex is at (-1 , 2), now let's get a point besides the vertex hmmm let's see it passes through (-2 , -1).

So we can reword that as what's the equation of a quadratic whose vertex is at (-1 , 2) and it passes through (-2 , -1)?

\(~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\begin{cases} h=-1\\ k=2\\ \end{cases}\implies y=a(~~x-(-1)~~)^2 + 2\hspace{4em}\textit{we also know that} \begin{cases} x=-2\\ y=-1 \end{cases} \\\\\\ -1=a( ~~-2-(-1) ~~ )^2 + 2\implies -3=a(-2+1)^2\implies -3=a \\\\\\ ~\hfill~ {\Large \begin{array}{llll} y=-3(x+1)^2 + 2 \end{array}} ~\hfill~\)

Answer:

y = -3(x + 1)^2 + 2

Step-by-step explanation:

y = a(x - h)^2 + k is the vertex form of a quadratic, where

Finding (h, k):

We see from the graph that the vertex is a maximum and its coordinates are (-1, 2).  Thus h is -1 and k is 2.  Since h becomes negative, it will be 1 in the parentheses: (x - (-1) = (x + 1).

Finding a:

In order to find a, we will need to plug in a point on the parabola for (x, y) and (-1, 2) for h and k.  We see that (0, -1) lies on the parabola so we can use this point for (x, y).

-1 = a(0 - (-1))^2 + 2

-1 = a(0 + 1)^2 + 2

-3 = a(1)^2

-3 = a

Thus, a = -3.

Thus, the exact equation in vertex form of the parabola is:

y = -3(x + 1)^2 + 2

I attached a picture from Desmos Graphing Calculator that shows how the equation I provided works and contains the two points you marked on the parabola, including (-1, 2) aka the maximum, and (0, -1) aka the y-intercept.

Answer:

Age of Anna = x years

Age of Jane i.e. Anna's sister = (x-y) years

a, What was the sum of their ages two years ago?

Solution,

Age of Anna two years ago = (x-2) years

Age of Jane two years ago = (x-y-2) years

Sum of their ages = x - 2 + x-y-2 = 2x - y -4

b. What will be the sum of their ages in 3 years?

Solution,

We have,

Present age of Anna = x years

Present age of Jane = (x-y) years

So,

Age of Anna after 3 years = (x+3) years

Age of Jane after 3 years = (x-y+3) years

Therefore,

Sum of their ages in 3 years = (x+3) +(x-y+3) = 2x - y+6

c. How old was Anna when Jane was born?

Solution,

Here,

According to question,

Jane is y years younger than Anna

So, Anna was y years when Jane was born.

[Suppose your age is 10 years and your brothers age is 14 years. You are 4 years younger than your brother. Also, his age was 4 years when you were born.]

Answer:

71.13

Step-by-step explanation:

71.13 would be 71.13 if it was rounded to the nearest cent.

To round 71.13 to the nearest cent consider the thousandths’ value of 71.13, which is 0 and less than 5. Therefore, the cents value of 71.13 remains at 3.

$71.13 rounded to the nearest cent = $71.13

Answer:

Nearest cent: $71.10

Nearest dollar: $71.00

Step-by-step explanation:

The nearest cent is $71.10 because you cannot round the three, so we are left with the one. The one cannot be rounded any higher because the 3 is so low. So, in conclusion, the answer is $71.10. If this wasn't the answer you were looking for, it is $71.00.

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The percentage of the distance Dominic is on the path is his distance

travelled as a fraction of the total distance when equivalent to 100.

The distance he has travelled on the path is 8.75 miles.

The given parameter are;

Length of Dominic's path = 12.5 miles

The length of the way Dominic is to the end = 70%

Required:

The distance Dominic has travelled on the path

The distance Dominic has travelled, D is 70% of 12.5 miles.

70% of 12.5 miles = 70% × 12.5 miles = 8.75 miles

The distance Dominic has travelled on the path, D = 8.75 miles

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To find the experimental probability for each outcome, we divide the number of times the cup lands in that position by the total number of tosses:

What is a outcome?

An outcome refers to a possible result of an experiment or event that is used to calculate the probability of that result occurring.

What is meant by experimental probability?

Experimental probability is the probability of an event based on actual, repeated trials or experiments rather than theoretical or mathematical calculations.

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\(1\frac{3}{4}\) feet as a multiplication expression using the unit, 1 foot, as a factor is \(1\frac{3}{4}\)×1.

The given fraction is \(1\frac{3}{4}\).

\(1\frac{3}{4}\) feet can be written as a multiplication expression as follows: 1 foot × 1 3/4. This is because \(1\frac{3}{4}\) is the same as 1 + 3/4.

Furthermore, 3/4 can be written as 0.75, which is the same as 0.75 × 1 foot.

Therefore, the multiplication expression is 1 foot × \(1\frac{3}{4}\) = 1 foot × (1 + 0.75) = 1 foot × 1 + 1 foot × 0.75 = 1 foot + 1.75 feet.

Therefore, \(1\frac{3}{4}\) feet as a multiplication expression using the unit, 1 foot, as a factor is \(1\frac{3}{4}\)×1.

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Step-by-step explanation:

1ft=12in

1¾ft=x

x=12×7/4=21in

1¾ft=1¾×1 ft

The equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.

To calculate the equivalent ratio of 1.25 : 3.75 : 7.5, we need to find a common multiplier that can be applied to all the numbers in the ratio to make them whole numbers. In this case, the common multiplier is 4 because it can be multiplied to each number to eliminate the decimals.

By multiplying each number in the ratio by 4, we get:

1.25 * 4 = 5

3.75 * 4 = 15

7.5 * 4 = 30

So the equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.

This means that the relative sizes or quantities represented by the original ratio are maintained in the equivalent ratio. For example, if we had 1.25 units of something, it would be equivalent to 5 units in the new ratio, and if we had 7.5 units, it would be equivalent to 30 units in the new ratio.

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Answer: 5 pounds

Step-by-step explanation:

Think about it in order to find j you multiply 6 times c. If j=30 you divide 30 from 6 to find the value of c. This is why c is 5.

Hope this helps :)

Answer: 3 ≤ 47

Step-by-step explanation:

The inequality given is 3 ≤ 47.

To determine the solutions to this inequality, we need to find the values of x that satisfy the inequality.

Looking at the options provided:

x = 24: This is not a solution because 24 is less than 47.

x = 51: This is a solution because 51 is greater than or equal to 47.

x = 6: This is not a solution because 6 is less than 47.

x = 99: This is a solution because 99 is greater than or equal to 47.

Therefore, the solutions to the inequality 3 ≤ 47 are x = 51 and x = 99.

The numeric values of the composite functions are given as follows:

The composite function of f(x) and g(x) is given by the following rule:

(f ∘ g)(x) = f(g(x)).

It means that the output of the inside function serves as the input for the outside function.

Then the numeric values of the composite functions are given as follows:

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Answer

37

Step by Step explanation

replace x with -7

which gives

-(-7)^2-10(-7)+16

= 37

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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The region common to both the inequality graphs represents the possible solutions for the given set of inequality.

Given is that Mayerlin has {x} dimes and {y} nickels. She has no more than 20 coins worth no less than $1.30 combined

We can write the inequalities as -

x + y < 20                         .... (1)

x/10 + y/20 > 1.30             .... (2)

Refer to the graph of the inequalities attached. The region common to both the inequality graphs represents the possible solutions for the given set of inequality.

Therefore, the region common to both the inequality graphs represents the possible solutions for the given set of inequality.

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The set of ordered pairs that represents a function is (D) {(-6, -3), (-4, -3), (-3, -3), (-2, -3), (0, 0)}.

A set of ordered pairs represents a function if each unique input (x-value) is associated with only one output (y-value).

{(-4, -3), (-2, -1), (-2, 0), (0, -2), (0, 2)}

In this set, both (-2, -1) and (-2, 0) have the same x-value but different y-values. Therefore, this set does not represent a function.

{(-5, -5), (-5, -4), (-5, -3), (-5, -2), (-3,0)}

In this set, all the ordered pairs have the same x-value (-5). Since (-5, -5), (-5, -4), (-5, -3), and (-5, -2) have the same x-value but different y-values, this set does not represent a function.

{(-4, -5), (-4, 0), (-3, -4), (0, -3), (3, -2)}

In this set, (-4, -5) and (-4, 0) have the same x-value but different y-values. Therefore, this set does not represent a function.

{(-6, -3), (-4, -3), (-3, -3), (-2, -3), (0, 0)}

In this set, each unique x-value is associated with a single y-value. There are no repeated x-values. Therefore, this set represents a function.

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Answer:

if it's m^2-16, than it's B, (m+4)(m-4)

Step-by-step explanation:

remember (a+b)(a-b)=a^2-b^2, or m^2-4^2=m^2-16

The table with correct values of A, B and C is,

⇒ Donuts   2        4        5        8

    Cost     13.80 27.60 34.50 55.20

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.

We have to given that;

The table below shows the ratios of boxed donuts to the cost.

Donuts    A       4        5     C

Cost    13.80  27.60   B   55.20

Now, By definition of ratio, we get;

⇒ A / 13.80 = 4 / 27.60

⇒ A = 13.80 × 4 / 27.60

⇒ A = 2.00

And,

⇒ 4 / 27.60 = 5 / B

⇒ B = 5 × 27.60 / 4

⇒ B = 34.5

⇒ 4 / 27.60 = C / 55.20

⇒ C = 55.20 × 4 / 27.60

⇒ C = 8

Thus, The table with correct values of A, B and C is,

⇒ Donuts   2        4        5        8

    Cost     13.80 27.60 34.50 55.20

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Answer:

a

Step-by-step explanation:

i took the test :)

Answer:

19 6/8 or 19 3/4

I’m not sure if you want the smallest possible fraction or not. If you don’t know just put the second one. K.

15.1.

181.2

Hope this helps.

Answer:

Step-by-step explanation:

y=kx²

y₁=k(1)²=k

y₃=k(3)²=9k

y₁-y₃=k-9k=32

-8k=32

k=-4

y=-4x²

y₋₂=-4(-2)²=-16